Details

Time bar (total: 9.9s)

sample60.0ms

Algorithm
intervals
Results
27.0ms68×body1280valid
14.0ms63×body640valid
5.0ms20×body2560valid
3.0ms25×body320valid
2.0ms64×body80valid
1.0ms16×body160valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
079
1108
done108

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.8b

localize6.0ms

Local error

Found 3 expressions with local error:

1.0b
(+ x (sqrt (+ (* x x) 1.0)))
3.8b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.0b
(sqrt (+ (* x x) 1.0))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u fma-def flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow hypot-def
Counts
3 → 52
Calls
3 calls:
17.0ms
(+ x (sqrt (+ (* x x) 1.0)))
19.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
10.0ms
(sqrt (+ (* x x) 1.0))

series278.0ms

Counts
3 → 9
Calls
3 calls:
68.0ms
(+ x (sqrt (+ (* x x) 1.0)))
165.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
44.0ms
(sqrt (+ (* x x) 1.0))

simplify1.2s

Counts
61 → 61
Iterations

Useful iterations: done (1.2s)

IterNodesCost
0139813
1329677
2938609
33024595
done5000593

prune185.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize11.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

series154.0ms

Counts
1 → 3
Calls
1 calls:
154.0ms
(fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))))

simplify821.0ms

Counts
13 → 13
Iterations

Useful iterations: done (820.0ms)

IterNodesCost
025295
151295
2171256
3989256
done5000255

prune39.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.3b
(/ 0.125 (pow x 3))
10.9b
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

rewrite138.0ms

Algorithm
rewrite-expression-head
Rules
888×times-frac
633×add-sqr-sqrt
608×*-un-lft-identity
602×add-cube-cbrt
520×prod-diff
131×unpow-prod-down cube-prod
55×div-inv
45×sqr-pow
43×cube-mult unpow3
13×fma-neg
12×associate-/r*
10×difference-of-squares
9×add-exp-log
5×add-cbrt-cube add-log-exp
4×pow1
3×expm1-log1p-u log-prod div-exp log1p-expm1-u associate-/l*
2×distribute-lft-out--
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg diff-log rem-log-exp pow-exp clear-num log-pow frac-sub flip--
Counts
3 → 641
Calls
3 calls:
69.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
8.0ms
(/ 0.125 (pow x 3))
1.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

series274.0ms

Counts
3 → 9
Calls
3 calls:
87.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
36.0ms
(/ 0.125 (pow x 3))
151.0ms
(log (fma 2 x (- (/ 0.5 x) (/ 0.125 (pow x 3)))))

simplify1.5s

Counts
650 → 650
Iterations

Useful iterations: done (1.4s)

IterNodesCost
074231264
1157025431
2326916537
done500015817

prune551.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
12.9b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.0b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite389.0ms

Algorithm
rewrite-expression-head
Rules
480×*-un-lft-identity
367×times-frac
244×add-sqr-sqrt
218×add-cube-cbrt
200×prod-diff
84×distribute-lft-out
80×unpow-prod-down
68×cube-prod
40×fma-neg
28×sqr-pow
22×cube-mult unpow3
19×associate-/r*
15×add-exp-log
11×log-prod
10×difference-of-squares
9×add-log-exp
8×add-cbrt-cube div-inv
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 408
Calls
4 calls:
7.0ms
(/ 0.0625 (pow x 5))
8.0ms
(/ 0.125 (pow x 3))
161.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
184.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series333.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(/ 0.0625 (pow x 5))
36.0ms
(/ 0.125 (pow x 3))
183.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
61.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify1.3s

Counts
420 → 420
Iterations

Useful iterations: done (1.3s)

IterNodesCost
046617336
1101511891
227829369
done50008909

prune568.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.8b

bsearch88.0ms

Steps
ItersRangePoint
11
6.1632953816490534e-12
2923699147.8271213
0.8969712032463295
10
-21283307590.397102
-3.152803306627408e-07
-1.0282378261696905

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03355
13555
done3555

end0.0ms

sample1.9s

Algorithm
intervals
Results
947.0ms2341×body1280valid
373.0ms1576×body640valid
205.0ms779×body2560valid
105.0ms780×body320valid
62.0ms2121×body80valid
31.0ms403×body160valid